Axions
159
and the interaction cross section for
aN~X
(5.81)
can be confidently estimated and collectively they require [181
ma $ 50keV.
(5.82)
Thus, if the solution of the strong CP problem is to be found using the PQ
mechanism, the axion must be 'invisible' in these experiments. All models which
achieve this use an SU(3) x SU(2) x U(I) singlet scalar field {1 having a nonzero U(l)PQ charge, which acquires a large VEV (vPQ » v) so that the beam
dump bound is satisfied. One way to achieve the invisibility is if the known
quarks and leptons have zero U(1)PQ charge but there exist some new quarks
(X), presumably very heavy, having non-zero PQ charge. Such a possibility
was proposed by Kim [191 and by Shifman et al [20] and the axion is called
the 'KSVZ' or 'hadronic' axion. The coupling to the scalar field {1 is given by
£KSVZ = -hXL{1XR +h.c.
(5.83)
and there is no (tree-level) coupling to the leptons. Another possibility. suggested
by Dine et al [21] and by Zhitnitskii [22], is that the known quarks and leptons do
carry PQ charge so, as in the original model, two Higgs doublets HI.2 are required
but they are coupled to the PQ field (1 only via a term in the Higgs potential having
the form.
V DFSZ = AHfir2H2{1 + h.c.
(5.84)
This was discussed in [51. The axion in this model is called the 'DFSZ' or 'GUT'
axion. Although differing considerably in their physical input, the models make
similar predictions for the coupling strength gy of the axion to two photons:
g~SVZ = _ 0.96
g~FSZ = 0.37.
5.3.3 Astrophysical constraints on axions
The experimental requirement discussed earlier that axions, if they exist, must
be 'invisible' implies that their coupling to photons, leptons and hadrons is very
weak. This is most naturally achieved by making fa '" VPQ very large which,
from (5.64) in turn entails ma being very small. For example, for a GUT axion,
we might expect fa '" VPQ '" VGUT = 0(10 15 GeV) and then (5.64) gives
ma -10- 8 e V. In principle, any weakly interacting particle having a mass smaller
than typical stellar temperatures, i.e. in the keV-MeV range, can provide an
additional mechanism for a star to cool, besides the standard neutrino emission.
Of course, the interactions must be strong enough to ensure sufficiently copious
production of the particle so that large amounts of energy can be carried away
159
and the interaction cross section for
aN~X
(5.81)
can be confidently estimated and collectively they require [181
ma $ 50keV.
(5.82)
Thus, if the solution of the strong CP problem is to be found using the PQ
mechanism, the axion must be 'invisible' in these experiments. All models which
achieve this use an SU(3) x SU(2) x U(I) singlet scalar field {1 having a nonzero U(l)PQ charge, which acquires a large VEV (vPQ » v) so that the beam
dump bound is satisfied. One way to achieve the invisibility is if the known
quarks and leptons have zero U(1)PQ charge but there exist some new quarks
(X), presumably very heavy, having non-zero PQ charge. Such a possibility
was proposed by Kim [191 and by Shifman et al [20] and the axion is called
the 'KSVZ' or 'hadronic' axion. The coupling to the scalar field {1 is given by
£KSVZ = -hXL{1XR +h.c.
(5.83)
and there is no (tree-level) coupling to the leptons. Another possibility. suggested
by Dine et al [21] and by Zhitnitskii [22], is that the known quarks and leptons do
carry PQ charge so, as in the original model, two Higgs doublets HI.2 are required
but they are coupled to the PQ field (1 only via a term in the Higgs potential having
the form.
V DFSZ = AHfir2H2{1 + h.c.
(5.84)
This was discussed in [51. The axion in this model is called the 'DFSZ' or 'GUT'
axion. Although differing considerably in their physical input, the models make
similar predictions for the coupling strength gy of the axion to two photons:
g~SVZ = _ 0.96
g~FSZ = 0.37.
5.3.3 Astrophysical constraints on axions
The experimental requirement discussed earlier that axions, if they exist, must
be 'invisible' implies that their coupling to photons, leptons and hadrons is very
weak. This is most naturally achieved by making fa '" VPQ very large which,
from (5.64) in turn entails ma being very small. For example, for a GUT axion,
we might expect fa '" VPQ '" VGUT = 0(10 15 GeV) and then (5.64) gives
ma -10- 8 e V. In principle, any weakly interacting particle having a mass smaller
than typical stellar temperatures, i.e. in the keV-MeV range, can provide an
additional mechanism for a star to cool, besides the standard neutrino emission.
Of course, the interactions must be strong enough to ensure sufficiently copious
production of the particle so that large amounts of energy can be carried away